If you find someones wallet in the street. Take the cash then give it back. If it can be proven you took the money, you can be charged with theft. The famous saying 'possession is 9/10ths of the law' relates to proving who's possession something is, not what your rights are once you have it.
The laws regarding found property greatly vary between countries. In some places, if you find something and you it's not possible to determine who the owner is, the founder can keep the found property. In other places, if you cannot determine the ownership of a found property, you have to hand it over to the police, otherwise you could be charged with theft. It's a complicated matter.
However, generally, if you find, say for instance, a wallet in a public thrash can and you can determine the identity of the owner (because, for example, there is a driving license in it), you cannot keep it.